Hierarchical Equations of Motion for Quantum Chemical Dynamics: Recent Methodology Developments and Applications.

ConspectusQuantum effects are critical to understanding many chemical dynamical processes in condensed phases, where interactions between molecules and their environment are usually strong and non-Markovian. In this Account, we review recent progress from our group in development and application of the hierarchical equations of motion (HEOM) method, highlighting its ability to address some challenging problems in quantum chemical dynamics.In the HEOM method, the bath degrees of freedom are represented using effective modes from exponential decomposition of the bath correlation function.

Simulating the operation of a quantum computer in a dissipative environment.

The operations of current quantum computers are still significantly affected by decoherence caused by interaction with the environment. In this work, we employ the non-perturbative hierarchical equations of motion (HEOM) method to simulate the operation of model quantum computers and reveal the effects of dissipation on the entangled quantum states and on the performance of well-known quantum algorithms. Multi-qubit entangled states in Shor's factorizing algorithm are first generated and propagated using the HEOM.

Sum-frequency vibrational spectroscopy of centrosymmetric molecule at interfaces.

The centrosymmetric benzene molecule has zero first-order electric dipole hyperpolarizability, which results in no sum-frequency vibrational spectroscopy (SFVS) signal at interfaces, but it shows very strong SFVS experimentally. We perform a theoretical study on its SFVS, which is in good agreement with the experimental results. Its strong SFVS mainly comes from the interfacial electric quadrupole hyperpolarizability rather than the symmetry-breaking electric dipole, bulk electric quadrupole, and interfacial and bulk magnetic dipole hyperpolarizabilities, which provides a novel and completely unconventional point of view.

Efficient and stereodivergent synthesis of deoxyimino sugars.

Both cis- and trans-2-substituted-1,2,3,6-tetrahydro-pyridin-3-ols have been prepared via an aldol condensation-ring-closing metathesis sequence. A stereodivergent synthesis of optionally functionalized deoxyimino sugars was achieved via asymmetric dihydroxylation or epoxidation/nucleophilic substitution of these tetrahydropyridines.